Job control lets you put it in the background and get it back in foreground again:
time ( set -m; sleep 10 & echo $! ; fg >/dev/null ; )
Hmm … the complete command winds up as a stopped job, though. Odd. Here's a workaround:
bash -c ' time ( set -m; sleep 10 & echo $! ; fg >/dev/null ; ) '
Of course, by then it might as well be:
bash -c ' time { set -m; sleep 10 & echo $! ; fg >/dev/null ; } '
I'd prefer avoiding that bash -c, but I'm kinda fresh out of ideas. :-\